Small drops of the pure linear alcohol ethoxylates C12E5 and C12E6 were injected into water at temperatures below their cloud points, and the times required for their dissolution were measured using videomicroscopy. Separately the rates of growth of the various liquid crystalline intermediate phases formed during penetration experiments with these surfactants in vertical linear cells were measured using videomicroscopy. It was found from both types of experiments that the dissolution process was controlled by diffusion, not by kinetics of phase transformation at interfaces. Effective diffusivities of the various phases were calculated from the data obtained and were found to be of order 10-10 m2/s. Finally, interferometry was used to measure concentration distributions as a function of time during dissolution of the lamellar phase of C12E5. Diffusivity in the micellar solution was found to increase with increasing surfactant concentration with a further increase occurring at the concentration where the lamellar phase formed. The results were consistent with the effective diffusivities determined from the videomicroscopy experiments and with available values in the literature obtained by other techniques.